International Journal of Modern Physics E

The accurate knowledge of the nuclear level density is crucial for understanding the nuclear structure and for numerous applications including astrophysical reactions. In this review paper, we discuss the shell-model description of the nuclear level density, the use of the statistical moments method and underlying physics. The level density found with the moments method is shown to agree with the results of the exact diagonalization of the Hamiltonian matrix. The statistical approach is also compared to other standard methods for deriving level densities. The role of specific interaction matrix elements is reviewed in connection to the behavior of the level densities as these evolve. Chaotization and thermalization processes, collective enhancement and phase transitions are discussed with changing strengths of specific groups of two-body interaction matrix elements. The popular phenomenological constant temperature model is compared to the moments method and the effective temperature parameter of the model for different isotopes is discussed.

The spectroscopic factor (SF) of doubly-magic nuclei, neutron shell closed and neutron-rich nuclei has been determined through ($d$, $p$) reaction in the projectile energy range from 3 to 26MeV. The theoretical angular differential cross-sections of ($d$, $p)$ reactions in scattering center-of-mass angles from $0^{\circ }$ to $60^{\circ }$ have been calculated using FRESCO and NRV-DWUCK5 codes. By comparing the theoretical angular differential cross-sections with available experimental angular differential cross-sections, the values of SF have been determined. The exponential increase of SF as a function of neutron separation energy normalized by spin of the recoil nuclei has been shown for the first time for doubly-magic nuclei. The similar type of trend has also been observed for neutron-rich as well as neutron shell closed nuclei as a function of neutron separation energy normalized by asymmetric factor of recoil nucleus. More experimental data are required to verify the trend predicted by this investigation.

Vibrational-rotation levels of the yrast and first nonyrast alternating-parity bands of the lanthanide ${}^{150}$Nd, ${}^{154}$Sm, ${}^{154,160}$Gd, ${}^{162,164}$Er and actinide ${}^{228,232}$Th, ${}^{230,236,238}$U, ${}^{240}$Pu nuclei are studied in the framework of a nonadiabatic collective model of even–even nuclei with quadrupole and octupole deformations. The theoretical spectra are obtained through the use of Gauss and harmonic-oscillator (HO) potentials in the radial part of the Schrödinger equation which is taken in polar coordinates. The change of the surface deformation of the nucleus with the collective excitation energy is taken into account. The $\mathrm{\Delta }I=1$ staggering structure of the yrast alternating-parity bands is also considered. The theoretically obtained energy bands and staggering diagrams are in good agreement with the corresponding experimental data and point out the soft character of the collective quadrupole–octupole deformation mode manifesting in these nuclei.

The analytic solutions of the Schrodinger equation for the Woods–Saxon (WS) potential and also for the generalized WS potential are obtained for the $l$-wave nonrelativistic spectrum, with an approximated form of the WS potential and centrifugal term. Due to this fact that the potential is an exponential type and the centrifugal is a radial term, we have to use an approximated scheme. First, the Nikiforov–Uvarov (NU) method is introduced in brief, which is a systematical method, and then Schrodinger equation is solved analytically. Energy eigenvalues and the corresponding eigenvector are derived analytically by using the NU method. After that, the generalized WS potential is discussed at the end.

The $\alpha$-decay chain of ${}^{314-340}126$ and ${}^{350-400}138$ is studied using cubic plus proximity potential with improved transfer matrix (CPP-ITM) model. The nuclear mass models DD-PC1, WS4, WS3.3 are employed to evaluate the $\alpha$-decay energies. Thus calculated $\alpha$-decay half-lives and decay chain lengths are found to be in good agreement with other theoretical formalisms. The spontaneous fission (SF) half-lives are calculated using the formalism of Xu et al. [Phys. Rev. C 71 (2005) 014309; Phys. Rev. C 78 (2008) 044329] to have a vision on the possible decay modes and decay chain lengths, and the most probable decay chains associated with the isotopes of $Z=126$ $\&$ $138$. This paper unveils the mass region that survives fission and also predict the long $\alpha$-decay chains of $Z=126$ $\&$ $138$ with ${}^{314}126$ emitting 6$\alpha$, ${}^{316\&318}126$ emit 5$\alpha$ $\&$ ${}^{320}126$ 4$\alpha$ particles, while for ${}^{350,352,354,356\&358}138$ chains will have $8,7,6,5\alpha$ emission. The SF for $Z=126$ $\&$ $138$ occur at $A\ge 330$ and $A\ge 372$. These current predictions may pave way to detect/synthesize the most probable isotopes of the superheavy elements $Z=126$ $\&$ $138$ in the laboratory through future experiments.

The relativistic six-quark equations are found in the framework of the dispersion relation technique. The strange baryonia are constructed without the mixing of the quarks and antiquarks. The relativistic six-quark amplitudes of the strange baryonia with the open and hidden strange are calculated. The poles of these amplitudes determine the masses of strange baryonia. Seventeen masses of baryonia are predicted.

The possible formation of tensor condensates originated from a tensor-type interaction between quarks is investigated in the three-flavor Nambu–Jona–Lasinio model including the Kobayashi–Maskawa–’t Hooft interaction, which leads to flavor mixing. It is shown that independent two tensor condensates appear and a tensor condensate related to the strange quark easily occurs by the effect of the flavor mixing compared with one related to light quarks. Also, it is shown that the tensor condensate related to the strange quark appears at a slightly smaller chemical potential if the Kobayashi–Maskawa–’t Hooft interaction is included, due to the flavor mixing effect. It is also shown that the two kinds of tensor condensates may coexist in a certain quark chemical potential due to the flavor mixing.

The well known, one-parameter Davydov–Filippov model (DFM) or its variants have been used often to study the inter band $\gamma$-g B(E2) ratios for the triaxially deformed nuclei. Here, its application for the axially deformed nuclei with $\gamma$ less than $20^{\circ }$ is illustrated, which has not received attention so far. Instead of the usual practice of studying the gamma-ground B(E2) ratios, we focus on the absolute B(E2) values in DFM. It offers a wholly new role of the $\gamma$-variable in explaining the spectral features of the axially deformed nuclei. Further, it illustrates the intimate relationship of the $\gamma$ variable and the quadrupole deformation variable $\beta$. Additionally, a unified view of the various differing patterns of the variation of the $\gamma$-g B(E2) ratios versus $\gamma$ is presented.

The relativistic six-quark equations are found in the framework of the dispersion relation technique. The bottom baryonia are constructed without the mixing of the quarks and antiquarks. The relativistic six-quark amplitudes of the bottom baryonia with the open and hidden bottom are calculated. The poles of these amplitudes determine the masses of bottom baryonia. 19 masses of baryonia are predicted.

The shape phase crossover in the mean-field plus the geometric quadrupole–quadrupole and pairing model within two $j$-orbits is analyzed, for which a simple description of ${}^{103-110}$Sn confined in the lowest $1d_{5/2}$ and $0g_{7/2}$ orbits above the ${}^{100}$Sn core is demonstrated to reveal the crossover behavior of the model. It is shown that $B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_g^{+})$, $Q(4_1^{+})/Q(2_1^{+})$ and $B(E2;9/2_1^{+}\to 5/2_1^{+})/B(E2;11/2_1^{+}\to 7/2_1^{+})$, $Q(9/2_1^{+})/Q(7/2_1^{+})$ in this case may serve as effective order parameters for even–even and odd-A systems, respectively, from which the shape phase crossover from the rotation-like phase to the superconducting-like phase can be observed with variation of the number of valence neutrons.

Temperature is an important and commonly used parameter among others to study properties of matter created during high energy collisions of nuclei. Experimental data from JINR and UrQMD (version 3.3p2) model simulations have been used to estimate temperature and other properties of positive pions in collisions of deuteron with carbon nuclei at incident momentum of 4.2GeV/$c$ in this paper. Transverse mass and transverse momentum spectra have been used to get inverse slope parameter/temperature of said particles, with the help of some fitting equations. These equations are referred as Hagedorn Thermodynamic and Boltzmann Distribution functions. Such functions or equations are used to describe particles spectra. Temperature of positive pions has been found to be equal to $104\pm 2$ and $112\pm 2$MeV in experimental and model, respectively, using Hagedorn function. Results from both experimental and model calculations have also been compared with each other and thus most reliable fitting function has been suggested. It is found that Hagedorn Thermodynamic function is the most reliable function to get pions’ temperature in said collision system at given momentum. Similarly, results obtained in this paper have been compared with results from other experiments in the world and worthy conclusions have been reached and reported.

The new experimental data on various characteristics of the secondary charged pions produced in $n^{12}$C collisions at 4.2GeV/c are presented. A comparative analysis of the average multiplicities and various kinematic characteristics of the charged pions produced in $n^{12}$C and $p^{12}$C collisions at 4.2GeV/c is made. The experimental data are compared systematically with the predictions of the modified FRITIOF model.